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Preheat oven to 450°. Toast fennel seeds in a small dry skillet over medium heat, tossing often, until fragrant, about 4 minutes. Let cool.
Combine fennel seeds, garlic, paprika, and 2 Tbsp. oil in a small bowl. Season pork with salt and pepper and place in a resealable plastic bag. Add spice mixture; seal bag and turn to coat. Let sit at least 30 minutes.
Heat remaining 1 Tbsp. oil in a large ovenproof skillet, preferably cast iron, over medium-high heat. Cook pork chops until golden brown on 1 side, about 4 minutes; turn. Add potatoes and shallots to skillet; season with salt and pepper and toss to coat in pan drippings. Cook, tossing potatoes and shallots occasionally, until pork is golden brown on second side, about 4 minutes.
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ransfer to oven and roast until potatoes are tender and an instant-read thermometer inserted into thickest part of chops registers 135°, 10–15 minutes. (If potatoes need more time, transfer chops to a plate and continue to roast potatoes until tender; transfer chops back to skillet when potatoes are done.) Remove skillet from oven and mix in parsley and vinegar. Let pork chops rest 5 minutes in skillet.
Transfer chops to a cutting board; cut meat from bones and slice against the grain. Serve with potatoes, shallots, and any pan juices.
DO AHEAD- Pork chops can be marinated 1 day ahead. Keep chilled.
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